Solved papers for CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2007
done CEE Kerala Engineering Solved Paper-2007 Total Questions - 240
question_answer1) A train is moving at\[30\text{ }m{{s}^{-1}}\]in still air. The frequency of the locomotive whistle is 500 Hz and the speed of sound is\[345\text{ }m{{s}^{-1}}\]. The apparent wavelength of sound in front of and behind the locomotive are respectively
question_answer2) An open organ pipe is closed suddenly with the result that the second overtone of the closed pipe is found to be higher in frequency by 100 than the first overtone of the original pipe. Then the fundamental frequency of the open pipe is
question_answer3) A transverse wave is described by the equation\[y={{y}_{0}}\sin 2\pi \left( ft-\frac{x}{\lambda } \right).\]The maximum particle velocity is equal to four times the wave velocity, if
question_answer4) Charges\[+2q,+q\]and\[+q\]are placed at the comers A, B and C of an equilateral triangle ABC. If E is the electric field at the circumcentre O of the triangle, due to the charge\[+q\], then the magnitude and direction of the resultant electric field at O is
question_answer5) N identical drops of mercury are charged simultaneously to 10 V. When combined to form one large drop, the potential is found to be 40 V, the value of N is
question_answer7) The electrostatic potential energy between proton and electron separated by a distance \[1\overset{\text{o}}{\mathop{\text{A}}}\,\] is
question_answer8) The plates of a parallel plat capacitor with air as medium are separated by a distance of 8 mm. A medium of dielectric constant 2 and thickness 4 mm having the same area is introduced between the plates. For the capacitance to remain the same, the distance between the plates is
question_answer9) The resistance of a wire at room temperature \[30{}^\circ C\]is found to be\[10\,\Omega \]. Now to increase the resistance by 10%, the temperature of the wire must be [The temperature coefficient of resistance of the material of the wire is\[0.002/{}^\circ C\]]
question_answer10) In a closed circuit, the current I (in ampere) at an instant of time t (in second) is given by\[I=4-0.08t\]. The number of electrons flowing in 50 s through the cross-section of the conductor is
question_answer11) If\[{{R}_{1}}\]and\[{{R}_{2}}\]be the resistances of the filaments of 200 W and 100 W electric bulbs operating at 220 V, then\[\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)\]is
question_answer12) A potentiometer wire, 10 m long, has a resistance of\[40\,\Omega \]. It is connected in series with a resistance box and a 2 V storage cell. If the potential gradient along the wire is (0.1 mV/cm), the resistance unplugged in the box is
question_answer13) When a current I flows through a wire, the drift velocity of the electrons is v. When current 21 flows through another wire of the same material having double the length and double the area of cross-section, the drift velocity of the electrons will be
question_answer14) A uniform electric field and a uniform magnetic field exist in a region in the same direction. An electron is projected with a velocity pointed in the same direction. Then the electron will
A)
be deflected to the left without increase in speed
doneclear
B)
be deflected to the right without increase in speed
question_answer15) A galvanometer of resistance \[20\Omega \] shows a deflection of 10 divisions when a current of 1 mA is passed through it. If a shunt of\[4\,\Omega \] is connected and there are 50 divisions on the scale, the range of the galvanometer is
question_answer16) A conducting rod of 1 m length and 1 kg mass is suspended by two vertical wires through its ends. An external magnetic field of 2 T is applied normal to the rod. Now the current to be passed through the rod so as to make the tension in the wires zero is [Take\[g=10\text{ }m{{s}^{-2}}\]]
question_answer17) A circular coil of 5 turns and of 10 cm mean diameter is connected to a voltage source. If the resistance of the coil is \[10\,\Omega \]the voltage of the source so as to nullify the horizontal component of earths magnetic field of 30 A turn\[{{m}^{-1}}\]at the centre of the coil should be
A)
6 V, plane of the coil normal to magnetic meridian
doneclear
B)
2 V, plane of the coil normal to magnetic meridian
doneclear
C)
6 V, plane of the coil along the magnetic meridian
doneclear
D)
2 V, plane of the coil along the magnetic meridian
question_answer18) A paramagnetic substance of susceptibility \[3\times {{10}^{-4}}\]is placed in a magnetic field of\[4\times {{10}^{-4}}A{{m}^{-1}}\]. Then the intensity of .magnetization in the units of\[A{{m}^{-1}}\]is
question_answer19) A square coil of side 25 cm having 1000 turns is rotated with a uniform speed in a magnetic field about an axis perpendicular to the direction of the field. At an instant t, the emf induced in the coil is\[e=200\text{ }sin\text{ }100\text{ }\pi t\]. The magnetic induction is
question_answer20) A transformer has an efficiency of 80%. It is connected to a power input of 5 kW at 200 V. If the secondary voltage is 250 V, the primary and secondary currents are respectively
question_answer21) When a DC voltage of 200 V is applied to a coil of self-inductance\[\left( \frac{2\sqrt{3}}{\pi } \right)H,\] a current of 1 A flows through it. But by replacing DC source with AC source of 200 V, the current in the coil is reduced to 0.5 A. Then the frequency of AC supply is
question_answer22) In a L-R circuit, the value of L is\[\left( \frac{0.4}{\pi } \right)H,\]and the value of R is \[30\Omega \]. If in the circuit, an alternating emf of 200 V at 50 cycles/s is connected, the impedance of the circuit and current will be
question_answer23) The dielectric constant of air is 1.006. The speed of electromagnetic wave travelling in air is\[a\times {{10}^{8}}m{{s}^{-1}},\]where a is about
question_answer24) A. The wavelength of microwaves is greater than that of UV-rays. B. The wavelength of IR rays is lesser than that of UV-rays. C. The wavelength of microwaves is lesser than that of IR rays D. Gamma rays have shortest wavelength in the electromagnetic spectrum. Of the above statements
question_answer26) The position of final image formed by the given lens combination from the third lens will be at a distance of [\[{{f}_{1}}=+10\text{ }cm,\]\[{{f}_{2}}=-10cm,\]\[{{f}_{3}}=+30\text{ }cm\]]
question_answer27) A slit of width a is illuminated by red light of wavelength \[6500\overset{\text{o}}{\mathop{\text{A}}}\,\]. If the first minimum falls at\[\theta =30{}^\circ ,\] the value of a is
question_answer28) Two beams of light of intensity\[{{I}_{1}}\]and\[{{I}_{2}}\] interfere to give an interference pattern. If the ratio of maximum intensity to that of minimum intensity is\[\frac{25}{9}\], then\[\frac{{{I}_{1}}}{{{I}_{2}}}\]is
question_answer29) If the polarizing angle of a piece of glass for green light is\[54.74{}^\circ ,\]then the angle of minimum deviation for an equilateral prism made of same glass is [Given: \[tan\text{ }54.74{}^\circ =1.414\]]
question_answer30) When a monochromatic point source of light is at a distance 0.2 m from a photoelectric cell, the saturation current and cut-off voltage are 12.0 mA and 0.5 V. If the same source is placed 0.4 m away from the photoelectric cell, then the saturation current and the stopping potential respectively are
question_answer31) Consider the nuclear reaction \[{{X}^{200}}\to {{A}^{110}}+{{B}^{80}}\] binding energy per nucleon for\[X,\text{ }A\]and B are 7.4 MeV, 8.2 MeV and 8.1 MeV respectively, then the energy released in the reaction is
question_answer32) The natural boron of atomic weight 10.81 is found to have two isotopes \[{{B}^{10}}\] and \[{{B}^{11}}\]. The ratio of abundance of isotopes in natural boron should be
question_answer34) When the forward bias voltage of a diode is changed from 0.6 V to 0.7 V, the current changes from 5 mA to 15 mA. Then its forward bias resistance is
question_answer35) In common emitter amplifier, the current gain is 62. The collector resistance and input resistance are \[5\,k\,\Omega \]and\[500\,\Omega \]respectively. If the input voltage is 0.01 V, the output voltage is
question_answer37) The real time variation of input signals A and B are as shown below. If the inputs are fed into NAND gate, then select the output signal from the following.
question_answer43) The values of two resistors are\[{{R}_{1}}=(6\pm 0.3)k\Omega \]and\[{{R}_{2}}=(10\pm 0.2)k\Omega \]. The percentage error in the equivalent resistance when they are connected in parallel is
question_answer44) Two trains are moving with equal speed in opposite directions along two parallel railway tracks. If the wind is blowing with speed u along the track so that the relative velocities of the trains with respect to the wind are in the ratio\[1:2,\] then the speed of each train must be
question_answer45) Two balls are dropped to the ground from different heights. One ball is dropped 2 s after the other but they both strike the ground at the same time. If the first ball takes 5 s to reach the ground, then the difference in initial heights is\[(g=10m{{s}^{-2}})\]
question_answer46) A ball is thrown vertically upwards with a velocity of\[25\text{ }m{{s}^{-1}}\] from the top of a tower of height 30 m. How long will it travel before it hits ground?
question_answer47) A ball is projected from the ground at a speed of\[10\text{ }m{{s}^{-1}}\]making an angle of\[30{}^\circ \]with the horizontal. Another ball is simultaneously released from a point on the vertical line along the maximum height of the projectile. The initial height of the second ball is \[(g=10m{{s}^{-2}})\]
question_answer48) The sum of the magnitudes of two forces acting at a point is 18 N and the magnitude of their resultant is 12N. If the resultant is at \[{{90}^{{}^\circ }}\]with the smaller force, the magnitude of the forces in N are
question_answer49) The position of a particle is given by \[\overrightarrow{r}=\hat{i}+2\hat{j}-\hat{k}\]and its linear momentum is given by\[\overrightarrow{P}=3\hat{i}+4\hat{j}-2\hat{k}\]. Then its angular momentum, about the origin is perpendicular to
question_answer50) A mass of 6 kg is suspended by a rope of length 2 m from a ceiling. A force of 50 N in the horizontal direction is applied at the mid-point of the rope. The angle made by the rope with the vertical, in equilibrium is
question_answer51) A shell at rest at the origin explodes into three fragments of masses 1kg, 2 kg and m kg. The 1kg and 2 kg pieces fly off with speeds of\[5\text{ }m{{s}^{-1}}\] along x-axis and\[6\text{ }m{{s}^{-1}}\]along y-axis respectively. If the m kg piece flies off with a speed of\[6.5\text{ }m{{s}^{-1}},\]the total mass of the shell must be
question_answer52) If the road is unbanked and the coefficient of friction between the road and the tyres is 0.8, then the maximum speed with which an automobile can move around a curve of 84.5 m radius without slipping \[(g=10\text{ }m{{s}^{-2}})\]is
question_answer53) A rod AB of mass 10 kg and length 4 m rests on a horizontal floor with end A fixed so as to rotate it in vertical plane about perpendicular axis passing through A. If the work done on the rod is 100 J, the height to which the end B be raised vertically above the floor is
question_answer54) A particle is released from a height 5. At certain height its kinetic energy is three times its potential energy. The height and speed of the particle at that instant are respectively
question_answer55) An electric pump is used to fill an overhead tank of capacity \[9\,{{m}^{3}}\] kept at a height of 10 m above the ground. If the pump takes 5 min to fill the tank by consuming 10 kW power the efficiency of the pump should be (Take \[g=10\text{ }m{{s}^{-2}}\])
question_answer56) A sphere of mass m and radius r rolls on a horizontal plane without slipping with the speed u. Now, if it rolls up vertically, the maximum height it would attain will be
question_answer57) A simple pendulum is released from A as shown. If m and I represent the mass of the bob and length of the pendulum, the gain in kinetic energy at B is
question_answer58) If the earth were to contract such that its radius becomes one quarter, without change in its mass, the duration of one full day would be
question_answer59) A satellite is launched in a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 1.01R. The period of second satellite is longer than the first one (approximately) by
question_answer61) The escape velocity of a body on the surface of earth is 11.2 km/s. If the mass of the earth is doubled and its radius halved, the escape velocity becomes
question_answer62) A tank of height H is fully filled with water. If the water rushing from a hole made in the tank below the free surface, strikes the floor at maximum horizontal distance, then the depth of the hole from the free surface must be
question_answer63) The length of a rubber cord is\[{{l}_{1}}\]metre when the tension is 4 N and\[{{l}_{2}}\]metre when the tension is 6 N. The length when the tension is 9 N, is
question_answer64) A wire of natural length\[l,\]Youngs modulus Y and area of cross-section A is extended by\[x\]. Then the energy stored in the wire is given by
question_answer65) A piece of solid weighs 120 g in air, 80 g in water and 60 g in a liquid. The relative density of the solid and that of the liquid are respectively
question_answer66) A closed gas cylinder is divided into two parts by a piston held tight. The pressure and volume of gas in two parts respectively are (P, 5V) and (10P, V). If now the piston is left free and the system undergoes isothermal process, then the volume of the gas in two parts respectively are
question_answer67) A Carnot engine with sinks temperature at \[17{}^\circ C\] has 50% efficiency. By how much should its source temperature be changed to increase its efficiency to 60%?
question_answer70) In damped oscillations, the amplitude of oscillations is reduced to one-third of its initial value\[{{a}_{0}}\]at the end of 100 oscillations. When the oscillator completes 200 oscillations, its amplitude must be
question_answer71) A particle executes simple harmonic motion with a time period of 16 s. At time\[t=2\text{ }s,\]the particle crosses the mean position while at \[t=4s,\]its velocity is\[4\text{ }m{{s}^{-1}}\]. The amplitude of motion in metre is
question_answer73) The relative lowering of vapour pressure of a dilute aqueous solution containing nonvolatile solute is 0.0125. The molality of the solution is about
question_answer74) If the elevation in boiling point of a solution of 10 g of solute (mol. wt. = 100) in 100 g of water is\[\Delta {{T}_{b}},\]the ebullioscopic constant of water is
question_answer75) An alloy of Pb-Ag weighing 1.08 g was dissolved in dilute \[HN{{O}_{3}}\] and the volume made to 100 mL. A silver electrode was dipped in the solution and the emf of the cell set up \[Pt(s),{{H}_{2}}(g)|{{H}^{+}}(1\,M)||A{{g}^{+}}(aq)|Ag(s)\] was 0.62V. If\[E_{cell}^{o}=0.80\,V\]is the percentage of Ag in the alloy? \[[At\text{ }25{}^\circ C,\text{ }RT/F=0.06]\]
question_answer76) The standard oxidation potentials of Zn, Cu, Ag and Ni electrodes are\[+0.76,-0.34,-0.80\]and +0.25 V respectively. Which of the following reaction will provide maximum voltage?
question_answer77) The activation energy of exothermic reaction \[A\to B\] is\[80\text{ }kJ\text{ }mo{{l}^{-1}}\]. The heat of reaction is\[200\text{ }kJ\text{ }mo{{l}^{-1}}\]. The activation energy for the reaction\[B\to A\]\[(in\text{ }kJ\text{ }mo{{l}^{-1}})\]will be
question_answer78) At 500 K, the half-life period of a gaseous reaction at an initial pressure of 80 kPa is 350 s. When the pressure is 40 kPa, the half-life period is 175 s. The order of the reaction is
question_answer80) On adding one mL of solution of\[10%\text{ }NaCl\]to 10 mL of gold sol in the presence of 0.25 g of starch, the coagulation is just prevented. The gold number of starch is
question_answer82) Both\[C{{o}^{3+}}\]and\[P{{t}^{4+}}\]have a coordination number of six. Which of the following pairs of complexes will show approximately the same electrical conductance for their 0.001M aqueous solutions?
question_answer84) An aromatic hydrocarbon with empirical formula\[{{C}_{5}}{{H}_{4}}\]on treatment with concentrated \[{{H}_{2}}S{{O}_{4}}\]gave a monosulphonic acid. 0.104 g of the acid required 10 mL of\[\frac{N}{20}NaOH\]for complete neutralization. The molecular formula of hydrocarbon is
question_answer85) Under which one of the following conditions, does the reaction, \[CH\equiv CH+C{{H}_{3}}OH\xrightarrow[{}]{?}C{{H}_{3}}O-CH=C{{H}_{2}}\]take place?
question_answer86) Identify the product/s in the following reaction. \[3C{{H}_{3}}CH=C{{H}_{2}}\xrightarrow[{}]{B{{H}_{3}}}X\xrightarrow[{}]{{{H}_{2}}{{O}_{2}}/O{{H}^{-}}}\] \[product/s+{{H}_{3}}B{{O}_{3}}\]
question_answer101) The radius of the first Bohr orbit of hydrogen atom is \[0.529\overset{\text{o}}{\mathop{\text{A}}}\,\]. The radius of the third orbit of\[{{H}^{+}}\]will be
question_answer105) Which one of the following volume (V)- temperature (T) plots represents the behaviour of one mole of an ideal gas at one atmospheric pressure?
question_answer106) The cubic unit cell of Al (molar mass 27 g \[mo{{l}^{-1}}\]) has an edge length of 405 pm. Its density is\[2.7\text{ }g\text{ }c{{m}^{-3}}\]. The cubic unit cell is
question_answer115) The radioactive isotope of caesium\[-137\]of weight 8g was collected on 1st February, 2006 and kept in a sealed tube. On 1st July 2006 it was found that only 0.25 g of it remained. The half-life period of the isotope is
question_answer117) The age of a specimen t is related to the daughter/parent ratio of number of atoms (D / P) by the equation (\[\lambda =\]decay constant)
question_answer119) The equlibrium constant for the reaction \[2N{{O}_{2}}(g)2NO(g)+{{O}_{2}}(g)\]is\[2\times {{10}^{-6}}\]at\[185{}^\circ C\]. Then the equilibrium constant for the reaction,\[4NO(g)+2{{O}_{2}}(g)\]\[4N{{O}_{2}}(g)\]at the same temperature would be
question_answer122) Let Z denote the set of all integers and\[A=\{(a,b):{{a}^{2}}+3{{b}^{2}}=28,a,b\in z\}\]and\[B=\{(a,b):a>b,a,b\in z\}\]. Then the number of elements in\[A\cap B\]is
question_answer125) The period of the function\[f(x)={{a}^{\{\tan (\pi x)+x-[x]\}}},\]where\[a>0,[\,\,.\,\,]\]denotes the greatest integer function and\[x\]is a real number, is
question_answer126) If\[\omega \]is a complex cube root of unity, then the value of\[\sin \left\{ ({{\omega }^{10}}+{{\omega }^{23}})\pi -\frac{\pi }{6} \right\}\]is
question_answer128) Let\[{{z}_{1}}\]and\[{{z}_{2}}\]be the roots of the equation \[{{z}^{2}}+pz+q=0\]where p, q are real. The points represented by\[{{z}_{1}},{{z}_{2}}\]and the origin form an equilateral triangle, if
question_answer129) If\[\alpha ,\beta ,\gamma \]are the cube roots of a negative number p, then for any three real numbers,\[x,y,z\] the value of \[\frac{x\alpha +y\beta +z\gamma }{x\beta +y\gamma +z\alpha }\] is
question_answer132) If \[\alpha \] and \[\beta \] are the roots of the equation\[a{{x}^{2}}+\] \[bx+c=0,\text{ }\alpha \beta =3\] and a, b, c are in AP, then \[\alpha +\beta \]is equal to
question_answer133) If one root of the equation\[{{x}^{2}}+px+12=0\]is 4, while the equation\[{{x}^{2}}+px+q=0\]has equal roots, then the value of q is
question_answer138) If an infinite geometric series the first term is a and common ratio is r. If the sum of the series is 4 and the second term is 3/4 then (a, r) is
question_answer139) The sets\[{{S}_{1}},{{S}_{2}},{{S}_{3}},....\]are given by \[{{S}_{1}}=\left\{ \frac{2}{1} \right\},\] \[{{S}_{2}}=\left\{ \frac{3}{2},\frac{5}{2} \right\},{{S}_{3}}=\left\{ \frac{4}{3},\frac{7}{3},\frac{10}{3} \right\},\] \[{{S}_{4}}=\left\{ \frac{5}{4},\frac{9}{4},\frac{13}{4},\frac{17}{4} \right\},....\] Then the sum of the numbers in the set\[{{S}_{25}}\]is
question_answer140) If\[{{H}_{1}},{{H}_{2}}\]are two harmonic means between two positive numbers a and\[b(a\ne b),A\]and G are the arithmetic and geometric means between a and b, then\[\frac{{{H}_{2}}+{{H}_{1}}}{{{H}_{2}}{{H}_{1}}}\]is
question_answer142) If a, b, c are distinct positive numbers each being different from 1 such that \[({{\log }_{b}}a.{{\log }_{c}}a-{{\log }_{a}}a)\] \[+({{\log }_{a}}b.{{\log }_{c}}b-{{\log }_{b}}b)\] \[+({{\log }_{a}}c.{{\log }_{b}}c-{{\log }_{c}}c)=0,\]then \[abc\] is
question_answer143) If\[\alpha \]and\[\beta \]are the roots of the equation \[{{x}^{2}}+px+q=0\]and if the sum \[(\alpha +\beta )x-\frac{{{\alpha }^{2}}+{{\beta }^{2}}}{2}+{{x}^{2}}+\frac{{{\alpha }^{2}}+{{\beta }^{3}}}{3}{{x}^{3}}\] \[-\frac{{{\alpha }^{4}}+{{\beta }^{4}}}{4}{{x}^{4}}+.....\] exists, then it is equal to
question_answer146) If \[{{(1+x-3{{x}^{2}})}^{10}}=1+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+....\]\[+{{a}_{20}}{{x}^{20}},\]then\[{{a}_{2}}+{{a}_{4}}+{{a}_{6}}+....+{{a}_{20}}\]is equal to
question_answer147) The value of\[\left( \frac{^{50}{{C}_{0}}}{1}+\frac{^{50}{{C}_{2}}}{3}+\frac{^{50}{{C}_{4}}}{5}+.... \right.\]\[\left. +\frac{^{50}{{C}_{50}}}{51} \right)\]is
question_answer158) If\[p:4\]is an even prime number,\[q:6\]is a divisor of 12 and r : the HCF of 4 and 6 is 2, then which one of the following is true?
question_answer172) ABC is a right angled triangle wit\[\angle B=90{}^\circ ,\] \[a=6\text{ }cm\]. If the radius of the circumcircle is 5 cm, then the area of\[\Delta ABC\]is
question_answer174) The \[x-\]axis,\[y-\]axis and a line passing through the point A (6, 0) form a triangle ABC. If\[\angle A=30{}^\circ ,\]then the area of the triangle, in sq unit is
question_answer175) The midpoint of the line joining the points \[(-10,\text{ }8)\]and\[(-6,12)\]divides the line joining the points\[(4,-2)\]and\[(-2,4)\]in the ratio
question_answer177) The straight line\[3x+4y-5=0\]and \[4x=3y+15\]intersect at the point P. On these lines the points Q and R are chosen so that PQ = PR. The slopes of the lines QR passing through (1, 2) are
question_answer178) The equation of the line which is such that the portion of line segment intercepted between the coordinate axes is bisected at\[(4,-3),\]is
question_answer179) The acute angle between the lines joining the origin to the points of intersection of the line\[\sqrt{3}x+y=2\]and the circle is\[{{x}^{2}}+{{y}^{2}}=4,\]is
question_answer180) If the circle \[{{x}^{2}}+{{y}^{2}}+4x+22y+c=0\]bisects the circumference of the circle\[{{x}^{2}}+{{y}^{2}}-2x+\]\[8y-d=0,\] then\[c+d\]is equal to
question_answer181) Two diameters of the circle\[3{{x}^{2}}+3{{y}^{2}}-6x\]\[-18y-7=0\]are along the lines\[3x+y=q\] and\[x-3y={{c}_{2}}\].Then the value of\[{{c}_{1}}{{c}_{2}}\]is
question_answer183) Length of the tangents from the point\[(1,2)\]to the circles\[{{x}^{2}}+{{y}^{2}}+x+y-4=0\]and\[3{{x}^{2}}+\] \[3{{y}^{2}}-x-y-k=0\]are in the ratio\[4:3,\] then k is equal to
question_answer186) If for the ellipse\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1,\]\[y-\]axis is the minor axis and the length of the latus rectum is one half of the length of its minor axis, then its eccentricity is
question_answer187) If the ellipse\[\frac{{{x}^{2}}}{16}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\]and the hyperbola \[\frac{{{x}^{2}}}{100}-\frac{4{{y}^{2}}}{225}=1\]have the same directrices, then the value of\[{{b}^{2}}\]is
question_answer188) The position vectors of the points A and B with respect to O are\[2\hat{i}+2\hat{j}+\hat{k}\]and\[2\hat{i}+4\hat{j}+4\hat{k}\]. The length of the internal bisector of\[\angle BOA\]of\[\Delta AQB\]is
question_answer189) Given\[(\overrightarrow{a}\times \overrightarrow{b})\times (\overrightarrow{c}\times \overrightarrow{d})=5\overrightarrow{c}\times 6\overrightarrow{d},\]then the value of\[(\overrightarrow{a}.\overrightarrow{b})\times (\overrightarrow{a}+\overrightarrow{c}+2\overrightarrow{d})\]is
question_answer190) Let a, b and c be non-zero vectors such that\[(\overrightarrow{a}.\overrightarrow{b})\times \overrightarrow{c}=\frac{-1}{4}|\overrightarrow{b}||\overrightarrow{c}|\overrightarrow{a}.\]. If\[\theta \]is the acute angle between the vectors \[\vec{b}\] and \[\vec{c}\], then the angle between\[\overrightarrow{a}\]and\[\overrightarrow{c}\]is equal to
question_answer191) A vector of magnitude 12 unit perpendicular to the plane containing the vectors \[4\hat{i}+6\hat{j}-\hat{k}\] and\[3\hat{i}+8\hat{j}+\hat{k}\]is
question_answer192) Forces of magnitudes 3 and 4 unit acting along\[6\hat{i}+2\hat{j}+3\hat{k}\]and\[3\hat{i}-2\hat{j}+6\hat{k}\]respectively act on a particle and displace it from (2, 2, -1) to (4, 3, 1). The work done is
question_answer193) If ABCD be a parallelogram and M be the point of intersection of the diagonals. If O is any point, then\[\overset{\to }{\mathop{OA}}\,+\overset{\to }{\mathop{OB}}\,+\overset{\to }{\mathop{OC}}\,+\overset{\to }{\mathop{OD}}\,\]is
question_answer194) If D, E and F are the mid points of the sides \[\overset{\to }{\mathop{BC}}\,,\text{ }\overset{\to }{\mathop{CA}}\,\] and\[\overset{\to }{\mathop{AB}}\,\]respectively of the triangle ABC and G is the centroid of the triangle, then \[\overset{\to }{\mathop{GD}}\,+\overset{\to }{\mathop{GE}}\,+\overset{\to }{\mathop{GF}}\,\]is
question_answer197) If\[P(x,y,z)\]is a point on the line segment joining Q (2, 2, 4) and R (3, 5, 6) such that projections of\[\overrightarrow{OP}\]on the axes are\[\frac{13}{5},\frac{19}{5},\frac{26}{5}\]respectively, then P divides QR in the ratio
question_answer199) The angle between\[\overrightarrow{r}=(1+2\mu )\hat{i}+(2+\mu )\hat{j}+(2\mu -1)\hat{k}\]and the plane\[3x-2y+6z=0\](where u is a scalar) is
question_answer200) The length of the shortest distance between the two lines \[r=(-3\hat{i}+6\hat{j})+s(-4\hat{i}+3\hat{j}+2\hat{k})\]and\[\overrightarrow{r}=(-2\hat{i}+7\hat{k})+t(-4\hat{i}+\hat{j}+\hat{k})\]is
question_answer204) A random variable X takes values 0, 1, 2, 3,... with probability\[p(X=x)=k(x+1){{\left( \frac{1}{5} \right)}^{x}}\] where k is constant, then\[P\{X=0)\]is
question_answer205) Out of 15 persons 10 can speak Hindi and 8 can speak English. If two persons are chosen at random, then the probability that one person speaks Hindi only and the other speaks both Hindi and English is
question_answer209) Let\[[x]\]denote the greatest integer\[\le x\]. If\[f(x)=[x]\]and\[g(x)=|x|,\]then the value of \[f\left( g\left( \frac{8}{5} \right) \right)-g\left( f\left( -\frac{8}{5} \right) \right)\]is
question_answer210) If\[f(x)=\frac{{{\log }_{e}}(1+{{x}^{2}}\tan x)}{\sin {{x}^{3}}},x\ne 0\]is to be continuous at\[x=0,\]then\[f(0)\]must be defined as
question_answer215) If\[y=\underset{n\to \infty }{\mathop{\lim }}\,(1+x)(1+{{x}^{2}})(1+{{x}^{4}})\]\[...(1+{{x}^{2n}}\text{ })\]and\[{{x}^{2}}<1,\]then y is equal to
question_answer219) A man of 2 m height walks at a uniform speed of 6 km/h away from a lamp post of 6 m height. The rate at which the length of his shadow increases is
question_answer221) A missile is fired from the ground level rises\[x\]metres vertically upwards in t seconds where\[x=100t-\frac{25}{2}{{t}^{2}}.\]The maximum height reached is
question_answer237) The solution of the differential equation \[\frac{dy}{dx}=\frac{y}{x}+\frac{\phi \left( \frac{y}{x} \right)}{\phi \left( \frac{y}{x} \right)}\]is
question_answer239) If\[{{c}_{1}},{{c}_{2}},{{c}_{3}},{{c}_{4}},{{c}_{5}}\]and\[{{c}_{6}}\]are constants, then the order of the differential equation whose general solution is given by \[y={{c}_{1}}cos\]\[(x+{{c}_{2}})+{{c}_{3}}\sin (x+{{c}_{4}})+{{c}_{5}}{{e}^{x}}+{{c}_{6}}\]